He was the only child of Crozier Cordell Culp, an attorney, and his wife, Bethel Martin (née Collins) Culp.

He graduated from Berkeley High School, where he was a pole vaulter and took second place at the 1947 CIF California State Meet.

Culp attended the University of the Pacific in Stockton, California but did not graduate. He later attended Washington University in St. Louis, San Francisco State, and the University of Washington School of Drama, but never completed an academic degree.

Culp earned an international reputation for his role as Kelly Robinson on I Spy (1965–1968), the espionagetelevision series in which co-star Bill Cosby and he played secret agents.

Prior to that, he starred in the CBS/Four Star Western series Trackdown as Texas Ranger Hoby Gilman from 1957 to 1959.